Aging in the Treasure: Some Methods for Evaluating Content Words in Large Data Bases

1. Background
Because of the demographic changes brought
about by control both of fertility and infectious
diseases in humans, people are living longer. In
order to come to terms with these facts it is useful
to examine how society has viewed aging and old
people at various stages of history. The Trésor de
la Langue Française database contains roughly a
thousand primarily literary texts published between 1789 and 1964, that is to say the period
during which France developed from a feudal,
agrarian state to a modern industrial society. It is
of interest to examine the use of terms relating to
aging in this society, and, given the volume of
data, a statistical approach would seem warranted.
Methods of time series analysis are used to study
the theme of aging through frequency counts from
the Trésor. By simply plotting the frequency count
of a collection of the most frequently occurring
words evoking the thematic construct of age, it is
possible to see clearly the evolution of allusions to
aging in a substantial portion of modern French
literature and thus, by inference, the evolution of
attitudes regarding age in one western European
culture.
2. The Data
All numbers analyzed in this paper are drawn from
the Dictionnaire des Fréquences, published in
1971 by the Trésor de la Langue Française (Imbs).
The preface to this work explains that it is based
on 416 primarily literary texts published from the
Revolution (1789) to the late 19th century, and
586 late 19th and early 20th century texts. The
total number of words recorded is 70 million after
the exclusion of 2.2 million proper nouns and
foreign words.
Volume III of the Dictionnaire contains the frequencies of the most frequently occurring words
in the database divided into 15 time segments of
roughly ten years each, but varying on occasion
between 27 years (1789-1815), and 5 years (1933-
37). The 4,000 most frequent words in each time
segment were retained so that a total of 6947
words are covered. The number of words and the
number of texts included in each time segment are
not reported but it seems reasonable to estimate
that the number of texts per time segment varies
between 50 and 75, and the number of words
sampled between 4 and 6 million. Frequencies in
each time segment are normalized to a base of 10
million words to facilitate comparison between
segments.
The vocabulary of aging which will be examined
is made up of six words, âgé, vieillard, vieillesse,
vieilli, vieillir and vieux. The frequencies for
grand-père are furnished but those for grand-mère
are not, so it was decided not to include this word
in order not to introduce gender bias into the data.
3. Frequencies in the Data
In order to facilitate understanding of the data, the
relative frequencies found in the Dictionnaire
have been adjusted to a base of 100,000 words,
roughly the size of a substantial (300 page) novel.
The sum of the frequencies of the six words evoking aging in each time segment varies between
21.00 and 58.31. Ignoring any temporal relationship in the data, calculations show the mean of
sums is 38.29 and the standard deviation is 9.38.
The observed total frequencies thus fall between
-1.84 and +2.14 standard deviations from the
mean. Given 14 degrees of freedom, none of these
totals generate a t-statistic significant even at the
0.05 level. However, examination of a time series
plot of the total frequency reveals a striking pattern
of temporal relationship. There is thus a clear need
for more sophisticated statistical techniques, other
than those based on the assumption of independently distributed data, because that assumption leads to an inflated estimate of the sampling
variability of the total frequencies.
It is known that when a large number of measurements are made in a relatively homogeneous population, these measurements tend to have the
well-known Gaussian or normal distribution.
When a frequently occurring phenomenon is studied in a relatively small corpus, for example the
period in Zola’s novels, this tendency is also observed (Brunet).
With regard to the underlying distribution of the
data in this study, after removing temporal dependencies and structures, it is anticipated that the
distribution of resulting residuals from the data
will, by analogy, also tend to the Gaussian distribution.
4. Methodology
Even an unsophisticated technique such as plotting word frequencies as a function of the start of
time periods for passages assayed in the Trésor can
reveal much about the evolution of attitudes with
time. Details on the graphical analysis of time
series to suspect – if not detect – features such as
a trend, oscillations, or a random component can
be found in Kendall, Stuart and Ord (1983).
A more recent and powerful analytical tool is
available in the form of change-point analysis is
to determine the date at which a time series changes in a manner stipulated by a model thus allowing the researcher to speculate about possible
reasons for the date of change. Descriptions of
these statistical tools can be found in Kotz and
Johnson (1989).
5. Results
Given below is a time series plot for the frequency
of words per 100,000 for all words selected that
evoke the theme of aging.
The total vocabulary of aging tends to be used with
increasing frequency from 1789 to about 1880,
after which its use steadily decreases. It can be
noted that the period from the beginning of the
Revolution to the abdication of President MacMahon in 1879 was characterized by social unrest,
culminating in four revolutions, the industrialization of the country without a concomitant improvement in standards of living, and constant contest
between a reactionary and a forward looking view
of governmental structures (Wright).
The data indicate that these tensions correspond to
an increasing use of the vocabulary of aging until
a crisis point somewhere around 1880. After that
turning point, a liberal ideology generally dominates French society and outlook, something
which the data suggest brings about fewer allusions to aging.
The proportion of the use of vieillard (the only
clearly pejorative term) to the other vocabulary of
aging, has a different pattern as evidenced from
the time series plot (below) of the relative frequency of the word vieillard.
The frequency of vieillard decreases sharply from
1789 to the 1860s, after which time the use of this
word shows much smaller fluctuations in a continuing downward trend. The significance of this
pattern is perhaps prophetic, since 1860 cannot be
identified as a turning point in French history or
society. It may be that the decreasingly pejorative
vocabulary of aging is predicting the triumph of
liberalism which will not take place in the political
realm until late 1879. But clearly this phenomenon
requires more study.
6. Conclusion
The study of the vocabulary of aging in a Trésor
de la Langue Française database does lead to results of interest to the historian of French society.
This small preliminary study also demonstrates
the usefulness of the techniques of time series
analysis in general and the suggestion of success
for the application of both intervention model
analysis and change-point analysis in studying
content words in large databases.
Figure 1: Frequencies for the Theme of Aging
Figure 2: Frequencies for the Word Vieillard
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References
Brunet, Étienne, 1985. “La phrase de Zola.” La
Critique Littéraire et l’Ordinateur. Montréal:
Derval and Lenoble, pp. 111–57.
Imbs, Paul, 1971. Dictionnaire des Fréquences. 4
vols. Nancy: C.N.R.S.-T.L.F.
Kendall, Sir Maurice, Alan Stuart and J. Keith
Ord, 1983. The Advanced Theory of Statistics,
Volume 3, Design and Analysis, and Time
Series, Fourth Edition. New York: Macmillan.
Kotz, Samuel and Norman L. Johnson, 1989. Encyclopedia of Statistical Science. New York:
John Wiley and Son. Wright, Gordon, 1987.
France in Modern Times. 4th ed. New York:
Norton.